Signatures of wave erosion in Titan’s coasts

The shorelines of Titan’s hydrocarbon seas trace flooded erosional landforms such as river valleys; however, it is unclear whether coastal erosion has subsequently altered these shorelines. Spacecraft observations and theoretical models suggest that wind may cause waves to form on Titan’s seas, potentially driving coastal erosion, but the observational evidence of waves is indirect, and the processes affecting shoreline evolution on Titan remain unknown. No widely accepted framework exists for using shoreline morphology to quantitatively discern coastal erosion mechanisms, even on Earth, where the dominant mechanisms are known. We combine landscape evolution models with measurements of shoreline shape on Earth to characterize how different coastal erosion mechanisms affect shoreline morphology. Applying this framework to Titan, we find that the shorelines of Titan’s seas are most consistent with flooded landscapes that subsequently have been eroded by waves, rather than a uniform erosional process or no coastal erosion, particularly if wave growth saturates at fetch lengths of tens of kilometers.


Fig. S2 .
Fig. S2.Illustration of the procedure for "unraveling" a closed shoreline.(A) Schematic showing the measurement of azimuth (anti-clockwise angle, α) and alongshore distance between consecutive vectors connecting shoreline points.(B) Shoreline of an example model initial condition consisting of flooded river valleys (see Fig. 2A), with color indicating alongshore distance.(C) The cumulative change in azimuth between successive shoreline points as a function of alongshore distance, detrended to remove the change in azimuth of 2 radians around the closed shoreline.Before detrending, the azimuth only takes on discrete values in increments of 0.25 radians because of the model grid.Color indicates alongshore distance, as in B. (D) The integral of the detrended cumulative change in azimuth with respect to distance as a function of alongshore distance, representing the "unwrapped" shoreline.Color indicates alongshore position, as in B.

Fig. S3 .
Fig. S3.Wavelet power spectrum.(A) Wavelet power spectrum of the unwrapped shoreline in fig.S1D.(B) Global wavelet power spectrum of the unwrapped shoreline in fig.S1D.(C) Normalized wavelet power spectrum produced by dividing the spectrum for each position in A by the global spectrum in B.

Fig. S4 .
Fig. S4.Illustration of fetch area.Map shows a portion of the 8-connected shoreline of the example in Fig. 2A.For a point along the shoreline (red circle), we show the fetch area (black) and the angle-weighted fetch area (white).Both fetch areas are calculated with a saturation length of 48 grid cells.

Fig. S6 .
Fig. S6.Joint probability distribution functions (JPDFs) of shoreline roughness and normalized fetch area for example model simulations of three end-member coastal erosion processes.Shoreline maps are the same model simulations shown in Fig. 2: (A) model initial condition formed by flooding a landscape that was previously incised by rivers, (B) simulation of wave erosion after lake area has increased to 150% of its initial value, and (C) simulation of uniform erosion after lake area has increased to 150% of its initial value.JPDFs are approximated with two-dimensional histograms for (D) the shoreline in A, (E) the shoreline in B, and (F) the shoreline in C. The same JPDFs are plotted in (G-I) with the probability contours for the characteristic distributions of the corresponding processes (fig.S4A-C).

Fig. S7 .
Fig. S7.Mapped lakes on Earth.Shorelines (red) for Earth lakes plotted over (A-C) Band 8 of the associated Sentinel2 image or on (D-G) a map of the percent occurrence of surface water in each pixel (51).Lakes plotted are (A) Lake Rotoehu, New Zealand (NZ); (B) Kozjak Jezero, Croatia (HR); (C) Prošćansko Jezero, HR; (D) Fort Peck Lake, United States of America (USA);(E) Lake Murray, USA; (F) Sebago Lake, USA; and (G) Lake Lanier, USA.See table S4 for image information.

Fig. S11 .
Fig. S11.Ternary diagrams showing probabilities of the three shoreline formation process scenarios for mapped shorelines on Titan for different saturation fetch lengths.Each panel has the same format as Figure 4 but assumes (A-F) waves that saturate at the indicated fetch length, or (G) fetch-limited conditions.(B) is the same as the dark magenta points in Figure 4; (G) is the same as the light magenta points in Figure 4. Figures made using Ternplot(60).
Fig. S11.Ternary diagrams showing probabilities of the three shoreline formation process scenarios for mapped shorelines on Titan for different saturation fetch lengths.Each panel has the same format as Figure 4 but assumes (A-F) waves that saturate at the indicated fetch length, or (G) fetch-limited conditions.(B) is the same as the dark magenta points in Figure 4; (G) is the same as the light magenta points in Figure 4. Figures made using Ternplot(60).

Table S1 .
Input parameters for numerical model simulations using Numerical model of coastal Erosion by Waves and Transgressive Scarps (NEWTS) (41).